{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Created by Tirthajyoti Sarkar, Ph.D."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Affinity Propagation Clustering Technique\n",
    "\n",
    "Affinity Propagation creates clusters by sending messages between pairs of samples until convergence. **A dataset is then described using a small number of exemplars**, which are identified as those most representative of other samples. The messages sent between pairs represent the suitability for one sample to be the exemplar of the other, which is updated in response to the values from other pairs. This updating happens iteratively until convergence, at which point the final exemplars are chosen, and hence the final clustering is given.\n",
    "\n",
    "## The algorithm\n",
    "\n",
    "Let $x_1$ through $x_n$ be a set of data points, with no assumptions made about their internal structure, and let $s$ be a function that quantifies the similarity between any two points, such that $s(x_i, x_j) > s(x_i, x_k) \\text{ iff } x_i$ is more similar to $x_j$ than to $x_k$. For this example, the negative squared distance of two data points was used i.e. for points xi and xk, \n",
    "${\\displaystyle s(i,k)=-\\left\\|x_{i}-x_{k}\\right\\|^{2}} {\\displaystyle s(i,k)=-\\left\\|x_{i}-x_{k}\\right\\|^{2}}$\n",
    "\n",
    "The diagonal of s i.e. ${s(i,i)}$ is particularly important, as it represents the input preference, meaning how likely a particular input is to become an exemplar. When it is set to the same value for all inputs, it controls how many classes the algorithm produces. A value close to the minimum possible similarity produces fewer classes, while a value close to or larger than the maximum possible similarity, produces many classes. It is typically initialized to the median similarity of all pairs of inputs.\n",
    "\n",
    "The algorithm proceeds by alternating two message passing steps, to update two matrices:\n",
    "\n",
    "* The \"responsibility\" matrix *$R$* has values $r(i, k)$ that quantify how well-suited $x_k$ is to serve as the exemplar for $x_i$, relative to other candidate exemplars for $x_i$.\n",
    "\n",
    "* The \"availability\" matrix *$A$* contains values $a(i, k)$ that represent how \"appropriate\" it would be for $x_i$ to pick $x_k$ as its exemplar, taking into account other points' preference for $x_k$ as an exemplar.\n",
    "\n",
    "Both matrices are initialized to all zeroes, and can be viewed as log-probability tables. The algorithm then performs the following updates iteratively:\n",
    "\n",
    "First, responsibility updates are sent around: \n",
    "$$ {\\displaystyle r(i,k)\\leftarrow s(i,k)-\\max _{k'\\neq k}\\left\\{a(i,k')+s(i,k')\\right\\}} $$\n",
    "Then, availability is updated per\n",
    "\n",
    "$$ {\\displaystyle a(i,k)\\leftarrow \\min \\left(0,r(k,k)+\\sum _{i'\\not \\in \\{i,k\\}}\\max(0,r(i',k))\\right)} $$ \n",
    "for ${\\displaystyle i\\neq k}$ and\n",
    "$$ {\\displaystyle a(k,k)\\leftarrow \\sum _{i'\\neq k}\\max(0,r(i',k))} $$\n",
    "\n",
    "The iterations are performed until either the cluster boundaries remain unchanged over a number of iterations, or after some predetermined number of iterations. The exemplars are extracted from the final matrices as those whose 'responsibility + availability' for themselves is positive i.e.\n",
    "\n",
    "$${\\displaystyle (r(i,i)+a(i,i))>0} {\\displaystyle (r(i,i)+a(i,i))>0})$$\n",
    "\n",
    "## Pros and cons\n",
    "\n",
    "Affinity Propagation can be interesting as **it automatically chooses the number of clusters based on the data provided**. For this purpose, the two important parameters are the preference, which controls how many exemplars are used, and the damping factor which damps the responsibility and availability messages to avoid numerical oscillations when updating these messages.\n",
    "\n",
    "**The main drawback of Affinity Propagation is its complexity**. The algorithm has a time complexity of the order $O(N^2 T)$, where $N$ is the number of samples and $T$ is the number of iterations until convergence. Further, the memory complexity is of the order $O(N^2)$ if a dense similarity matrix is used, but reducible if a sparse similarity matrix is used. This makes Affinity Propagation most appropriate for small to medium sized datasets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make some synthetic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import AffinityPropagation\n",
    "from sklearn import metrics\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "\n",
    "# Generate sample data\n",
    "centers = [[1, 1], [-1, -1], [1, -1]]\n",
    "X, labels_true = make_blobs(n_samples=300, centers=centers, cluster_std=0.5,random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(300, 2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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k6NEyj3yvcOK8dmKws0DTVXlry8us3/QGeZPHcWXzWbq0qeHIaUFVrQII1u9V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\nwYzZTzN58uQmYzp16hS9OjQuaHYNuPQixF+VQVo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fqqilgt3cCd17W4WSTDwq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\nlFLKIzRoK6WUUh6hQVsppZTyiP8HI19tizmpRrkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22dd9cf7cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.scatter(X[:,0],X[:,1],edgecolors='k',c='orange',s=75)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Compute Affinity Propagation\n",
    "af_model = AffinityPropagation(preference=-50).fit(X)\n",
    "cluster_centers_indices = af_model.cluster_centers_indices_\n",
    "labels = af_model.labels_\n",
    "n_clusters_ = len(cluster_centers_indices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Number of detected clusters and their centers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of clusters detected by the algorithm: 3\n"
     ]
    }
   ],
   "source": [
    "print(\"Number of clusters detected by the algorithm:\", n_clusters_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster centers detected at:\n",
      "\n",
      " [[ 1.03325861  1.15123595]\n",
      " [ 0.93494652 -0.95302339]\n",
      " [-1.18459092 -1.11968959]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Cluster centers detected at:\\n\\n\", X[cluster_centers_indices])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5uW3bNlztbniJRg6Puwk9/rpgVq1adc5t0Wg0LFuxlJa9mrHZdTmH9LvIdN/P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\nIiIiPqHSFhER8Yn/AcKx72CEPFUcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22ddbd81048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.scatter(X[:,0],X[:,1],edgecolors='k',c=af_model.labels_,s=75)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### Homogeneity\n",
    "\n",
    "Homogeneity metric of a cluster labeling given a ground truth.\n",
    "\n",
    "A clustering result satisfies homogeneity if all of its clusters contain only data points which are members of a single class. This metric is independent of the absolute values of the labels: a permutation of the class or cluster label values won’t change the score value in any way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Homogeneity score: 0.871559529839\n"
     ]
    }
   ],
   "source": [
    "print (\"Homogeneity score:\", metrics.homogeneity_score(labels_true,labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Completeness\n",
    "\n",
    "Completeness metric of a cluster labeling given a ground truth.\n",
    "\n",
    "A clustering result satisfies completeness if all the data points that are members of a given class are elements of the same cluster. This metric is independent of the absolute values of the labels: a permutation of the class or cluster label values won’t change the score value in any way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Completeness score: 0.871585975337\n"
     ]
    }
   ],
   "source": [
    "print(\"Completeness score:\",metrics.completeness_score(labels_true,labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_new = [0.5,0.4]\n",
    "x_pred = af_model.predict([x_new])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New point (0.5,0.4) will belong to cluster 0\n"
     ]
    }
   ],
   "source": [
    "print(\"New point ({},{}) will belong to cluster {}\".format(x_new[0],x_new[1],x_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_new = [-0.5,0.4]\n",
    "x_pred = af_model.predict([x_new])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New point (-0.5,0.4) will belong to cluster 2\n"
     ]
    }
   ],
   "source": [
    "print(\"New point ({},{}) will belong to cluster {}\".format(x_new[0],x_new[1],x_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time complexity and model quality as the data size grows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import time\n",
    "from tqdm import tqdm "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████████████| 12/12 [04:10<00:00, 20.84s/it]\n"
     ]
    }
   ],
   "source": [
    "n_samples = [10,20,50,100,200,500,1000,2000,3000,5000,7500,10000]\n",
    "centers = [[1, 1], [-1, -1], [1, -1]]\n",
    "t_aff = []\n",
    "homo_aff=[]\n",
    "complete_aff=[]\n",
    "\n",
    "for i in tqdm(n_samples):\n",
    "    X,labels_true = make_blobs(n_samples=i, centers=centers, cluster_std=0.5,random_state=0)\n",
    "    t1 = time.time()\n",
    "    af_model = AffinityPropagation(preference=-50,max_iter=50).fit(X)\n",
    "    t2=time.time()\n",
    "    t_aff.append(t2-t1)\n",
    "    homo_aff.append(metrics.homogeneity_score(labels_true,af_model.labels_))\n",
    "    complete_aff.append(metrics.completeness_score(labels_true,af_model.labels_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9x9FHH817773HIYccwhdffJHrkCqNdBKD3YBZAGbWAOgNXOruFxDOSji5lOvZ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\nU2IgIiIiYf8fyOT+cUVhmj4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22ddce94470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Time complexity of Affinity Propagation\\n\",fontsize=20)\n",
    "plt.scatter(n_samples,t_aff,edgecolors='k',c='green',s=100)\n",
    "plt.plot(n_samples,t_aff,'k--',lw=3)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.xlabel(\"Number of samples\",fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.ylabel(\"Time taken for model (sec)\",fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ljBe0hAkkaovaxECkofU//vjjOhcODenfv3+9QOAXv/gFJSUlodZ/+OGHmTx5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\n6AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22d80068d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Homogeneity score with data set size\\n\",fontsize=20)\n",
    "plt.scatter(n_samples,homo_aff,edgecolors='k',c='green',s=100)\n",
    "plt.plot(n_samples,homo_aff,'k--',lw=3)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.xlabel(\"Number of samples\",fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.ylabel(\"Homogeneity score\",fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Czrlbgqqqm4F/mdm7+M5HZVQNMbwPMR2SnHPvmtnt+Oq/fwcdyzbjxxE4EP+DHN92lQ5z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\nMP8DSa8e7TMmtDAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22ddced6940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Completeness score with data set size\\n\",fontsize=20)\n",
    "plt.scatter(n_samples,complete_aff,edgecolors='k',c='green',s=100)\n",
    "plt.plot(n_samples,complete_aff,'k--',lw=3)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.xlabel(\"Number of samples\",fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.ylabel(\"Completeness score\",fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How well the cluster detection works in the presence of noise? Can damping help?\n",
    "\n",
    "Create data sets with varying degree of noise std. dev and run the model to detect clusters. Also, play with damping parameter to see the effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "noise = [0.01,0.05,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.25,1.5,1.75,2.0]\n",
    "n_clusters = []\n",
    "for i in noise:\n",
    "    centers = [[1, 1], [-1, -1], [1, -1]]\n",
    "    X, labels_true = make_blobs(n_samples=200, centers=centers, cluster_std=i,random_state=101)\n",
    "    af_model=AffinityPropagation(preference=-50,max_iter=500,convergence_iter=15,damping=0.5).fit(X)\n",
    "    n_clusters.append(len(af_model.cluster_centers_indices_))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Detected number of clusters: [200, 67, 1, 68, 60, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 9]\n"
     ]
    },
    {
     "data": {
      "image/png": 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9gXHA6aRk58QBxGNmZmaZwjc4ioiFpFsfD/X2x1dGxBUAkqYDG1UpNz8ibu5j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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22d8010e4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Detected number of clusters:\",n_clusters)\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Cluster detection with noisy data for low damping=0.5\\n\",fontsize=16)\n",
    "plt.scatter(noise,n_clusters,edgecolors='k',c='green',s=100)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.xlabel(\"Noise std.dev\",fontsize=15)\n",
    "plt.yticks(fontsize=15)\n",
    "plt.ylabel(\"Number of clusters detected\",fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "noise = [0.01,0.05,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.25,1.5,1.75,2.0]\n",
    "n_clusters = []\n",
    "for i in noise:\n",
    "    centers = [[1, 1], [-1, -1], [1, -1]]\n",
    "    X, labels_true = make_blobs(n_samples=200, centers=centers, cluster_std=i,random_state=101)\n",
    "    af_model=AffinityPropagation(preference=-50,max_iter=500,convergence_iter=15,damping=0.9).fit(X)\n",
    "    n_clusters.append(len(af_model.cluster_centers_indices_))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Detected number of clusters: [3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 5, 5, 6, 6, 7]\n"
     ]
    },
    {
     "data": {
      "image/png": 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ERKQG8j1o5aj0/2b2FWAX4GPxJ6RFzze/FbizkkGKiIhIbknPmZ8D/CDzUafR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\nSuYiIiIN7v8DwV7liWJgDdQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22d802441d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Detected number of clusters:\",n_clusters)\n",
    "plt.figure(figsize=(8,5))\n",
    "plt.title(\"Cluster detection with noisy data for high damping=0.9\\n\",fontsize=16)\n",
    "plt.scatter(noise,n_clusters,edgecolors='k',c='green',s=100)\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=15)\n",
    "plt.xlabel(\"Noise std.dev\",fontsize=15)\n",
    "plt.yticks([i for i in range(2,10)],fontsize=15)\n",
    "plt.ylabel(\"Number of clusters detected\",fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** We see that for low damping factor is not good for cluster detection as it creates oscillatory predictions. Higher damping stablizes the prediction. For low noise std. dev, the prediction is correct and for higher noise it deviates slowly.**"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
